Double Vision & Newton’s Dreams

Or, as I would have very much preferred to title it, Blake after Newton after Blake. A short note that’s taken me 18 months to get to print is now available at Oxford University Press; but it’s behind a subscription wall because my research budget couldn’t take the open-access fee. I believe this article is important for the general public perception of William Blake, so I am going to lay out the basic argument in a digestible format here; people can email me for the pdf if they want to read further.

Romanticism and Newtonianism:

When people use the word “romantic” to mean things like “irrational,” “emotional,” “excitable,” and “nostalgic,” they aren’t always thinking of the literary movement called Romanticism; but when they are, they are thinking of a clutch of poets’ failed rebellion against the unrelenting rationalism of modernity. They are thinking of John Keats tipsily toasting “Newton’s health and confusion to mathematics,” or William Blake praying to ward off a scientific flattening of his experiential world:

Now I a fourfold vision see
And a fourfold vision is given to me
Tis fourfold in my supreme delight
And three fold in soft Beulahs night
And twofold Always. May God us keep
From Single vision & Newtons sleep

Now, this anti-science sentiment is not current with Romantic scholarship. First, period scholars have labored for decades to uncover the social and philosophical ties between poets and scientists — a very accessible starting point is Richard Holmes’s bestselling, recent-ish Age of Wonder. Second, critically-minded historians of science have redefined what “science” was in the Romantic era, to show that it was very much a part of its time: politically radical, proto-industrial, and very social (these are rather academic but I can’t recommend them highly enough: Jan Golinski’s …Chemistry and Enlightenment and Robert Mitchell’s Experimental Life!). And then there’s a third group that I like to think of myself as a member of: people who professionally study and experiment with beauty and meaning. For us, this arts/sciences distinction has always seemed clumsy, and useful only to agents of dullness. For this third group, a thing can be (and most should be) studied in a thousand different ways. It’s our job to make things more meaningful, and to do that we oftentimes insist on the specificity of things to make them come alive in unexpected ways. No later than 1805, William Blake produced a sort of mythical portrait of Isaac Newton. This painting has achieved iconic status in the popular understanding of Romanticism as an artistic rebellion against “science” and Enlightenment rationalism:

The story goes like this: Newton is in a sort of dream space (undersea?); He is sitting on a wildly-colored, complex coral reef; but he doesn’t notice all this wild beauty, because he’s myopically focused on the simple geometrical exercise he’s performing. Newton is basically worshiping his own mental operations, which blinds him to the beautiful complexity of the world. As a result, he becomes almost physically deformed: he is hunched almost in half, and his muscles have an unsettling crispness to them, as though he is becoming a geometric diagram of some sort. In other words, people tend to understand this painting as a deeply satirical portrait of an absentminded mathematician, who loses the world around him in favor of an incredibly reductive model. But the artists and art historians and literary theorists who have studied this painting have been telling much more interesting stories about it for a long time:

Backstory on Blake’s Newton:

1) Donald Ault: A Convincing Illusion

Donald Ault was one of the first people to take seriously Blake’s obsession with Newton. In his classic book, he argued that Newton’s mathematics bothered Blake not because they were simple, but because they were so seductively complex. After all, Newton’s calculus had elevated geometry to the point where it could give very convincing accounts of some very complex physical phenomena. And so Blake’s fight with Newton was, more or less, to remind us that we’re looking at a model, and that there are alternative models.

An extension of this argument comes out of the 1970’s and 1980’s reevaluation of who Isaac Newton was. Newton wasn’t a mad mathematician who worshiped geometry; his unpublished works showed him instead to be an alchemist and spiritualist. This discoverer of gravity, for instance, believed that the planets moved because angels, singing to them, made them desire one another. In this telling, it is the generations separating Newton (died in 1726) and Blake (born in 1757) who turned him into a robotic math nerd by obsessing over his calculus. So, the argument goes, because Blake couldn’t have known about this unpublished, mystical Isaac Newton, he was actually in agreement with the real Newton that everyone had forgotten about!

2) W. J. T. Mitchell: Beauty and … Entropy

W. J. T. Mitchell, who has written some of the most enduringly thought-provoking and strange things about Blake, took some cues from Robert Essick on the history of coral and Blake’s lesser-known works. Scientists had just realized that coral was an animal, and that a reef was made of thousands of years of the animals’ excretions. Blake, doing hack-work, had illustrated a book on kidney stone operations, and those stones look a lot like his coral. In fact, Blake’s coral was printed in a semi-random, unorthodox way, by painting wood and slamming it on the canvas, before carving out shapes with ink later on.

And so Mitchell’s story is essentially that Newton is sitting on the toilet, doing a crossword puzzle. On the one hand, that makes Newton much sillier, but on the other, it brings him down to earth. Instead of a mythical battle between nature and abstraction, we have the basic human activity of negotiating between order and disorder. In other words, this is a painting about disentropy. And when we are very lucky, our mental operations are fun puzzles, and the byproducts of our human activities are colorful.

Blake’s Puzzle

My contribution to this long scholarly discussion about Blake’s Newton is to help show just how deep Blake’s technical knowledge of Newton’s system went. This will keep us from turning him into an anti-science, wild-eyed artist, and to better appreciate his experiments with abstraction. Led on by Ault, Mitchell, Essick, and others, I dug into the eighteenth-century history of Newton’s reception. In other words, if Blake was reading about Newton, who was he reading?

I. Bernard Cohen and Anne Whitman’s translation of Newton was an authoritative (a 370-page introduction!) introduction, and in this book, they left us this little gem. Newton sometimes left out the basic steps that went into his formulas, and in the case of his famous proof on gravity, he had assumed that his reader knew a whole section of geometry called “conics,” and so left the whole proof out. As a result, a cottage industry cropped up, of mathematicians showing this proof step-by-step. Sure enough, there are many, many treatises from the 1700’s on conic sections, or “conics.” The idea is that by taking a cone, and slicing it with a plane, you can generate any second-order curve. Images from Wikipedia.

And so when Newton proved that gravity obeyed a second-order law, he proved that the geometrical branch of conics could be used to generate any path in a two-body system. There are different ways of performing this proof. What I found was that some of these ways, in 18th-century geometrical manuals, involve steps whose diagrams look very similar to Blake’s. Here is James Milnes’ 1702 proof, alongside the hands of Blake’s Newton. (The link here goes to a 1723 edition).

What Milnes does here is shows us how to get planes tangent to the cone (ADE), in preparation for actually cutting the cone into curves. This technique is useful, he says, for finding the limits of curves. Almost concurrently with Blake’s 1805 painting, we see a similar construction appear in the 1807 illustrations for conics in Abraham Rees’ Cyclopaedia:

What is exciting about Rees’s construction is that it is built to give readers an intuitive way for taking the sections of a cone. Look at Figure 20, below. The long axis PQ on the ellipse runs parallel to the line VD. If we make AD shorter, by sliding D inwards, VD becomes steeper and steeper — if we keep PQ parallel with this line, we will eventually have not an ellipse, but a parabola, then a hyperbola. This technique, in other words, creates a sort of control to easily produce varying, complex curves.

This is a pretty obscure joke that Blake is making, but it allows us to rethink the painting in some important ways.

Blake would have gone much deeper into Newtonian mathematics than previously thought, in order to make this reference.

Newton’s geometrical exercise is not a simple triangle, anymore, and it’s not obviously less complex than the coral.

We are being asked to participate with Newton in the production of complexity, rather than standing back ironically and laughing at him. It takes work to get in on the joke: the viewer/user must actually do the work of visually imagining these shapes!

Fortunately, Blake’s/Milnes’/Rees’s construction makes it easy to imagine these curves. This is an act of assisted visual imagining.

Blake’s painting is invoked almost monthly as shorthand for an artistic, irrational rebellion against science, and it’s important to remember just how technically competent and incisive this rebellion could be. I hope this makes the contours of an involved literary debate more accessible to people — at least now it’s not behind a paywall! Feel free to email me with comments, questions, suggestions, or requests for the original pdf 🙂